Electrode formal

Fig. 2 Energy diagram of Tb(III) ion EL at oxide-covered aluminum electrode. Formal potentials of oxygen, hydrogen peroxide and oxyradicals at pH 5-6 ate used in the diagram [34]...

Conventional batteries consist of a liquid electrolyte separating two solid electrodes. In the Na/S battery this is inverted a solid electrolyte separates two liquid electrodes a ceramic tube made from the solid electrolyte sodium /5-alumina (p. 249) separates an inner pool of molten. sodium (mp 98°) from an outer bath of molten sulfur (mp 119°) and allows Na" " ions to pass through. The whole system is sealed and is encased in a stainless steel canister which also serves as the sulfur-electrode current collector. Within the battery, the current is passed by Na+ ions which pass through the solid electrolyte and react with the sulfur. The cell reaction can be written formally as... 

Rotating-disk voltammetry is the most appropriate and most commonly employed method for studying mediation. In most systems that have been studied, there has been little penetration of the substrate in solution into the polymer film. This can be demonstrated most easily if the polymer film is nonconductive at the formal potential of the substrate. Then the absence of a redox wave close to this potential for an electrode coated with a very thin film provides excellent evidence that the substrate does not penetrate the film significantly.143 For cases where the film is conductive at the formal potential of the substrate, more subtle argu-... 

If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrodes.9 Cyclic voltammograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for [Fe(CN)6]3 /4 in polypyrrole with a pyridinium substituent at the 1-position.243 This N-substituted polypyrrole does not become conductive until potentials significantly above the formal potential of the [Fe(CN)6]3"/4 couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed. 

In addition to the exchange current density the transfer coefficient a is needed to describe the relationship between the electrode potential and the current flowing across the electrode/solution interface. From a formal point of view a can be obtained by calculating the partial current densities with respect to the electrode potential for the anodic reaction ... 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

Parameter E° in Eqs. (3.30) and (3.32) is called the standard electrode potential it corresponds to the value of electrode potential that is found when the activities of the components are unity. Values E° differ somewhat from values E°. For a more distinct differentiation between these parameters, E° is called the formal electrode potential. 

Electrodes of the second type can formally be regarded as a special case of electrodes of the first type where the standard state (when E = °) corresponds not to flAg+ = 1 but to a value of == 10 mol/L, which is established in a KCl solution of unit activity. In this case, the concentration of the potential-determining cation can be varied by varying the concentration of an anion, which might be called the controlling ion. The oxides and hydroxides of most metals (other than the alkali metals) are poorly soluble in alkaline solutions hence, almost all metal electrodes in alkaline solutions are electrodes of the second type. 

In industrial electrochemical cells (electrolyzers, batteries, fuel cells, and many others), porous metallic or nonmetallic electrodes are often used instead of compact nonporous electrodes. Porous electrodes have large trae areas, S, of the inner surface compared to their external geometric surface area S [i.e., large values of the formal roughness factors y = S /S (parameters yand are related as y = yt()]. Using porous electrodes, one can realize large currents at relatively low values of polarization. 

This raises the electrochemical potential, of these molecules and alters the formal value of electrode potential in redox reactions involving the chlorophyll (see Section 29.4). 

Thiols are easily oxidized to disulfides in solution, but this reaction occurs only very slowly at most electrode surfaces. However, use can be made of the unique reaction between thiols and mercury to detect these compounds at very favorable potentials. The thiol and mercury form a stable complex which is easily oxidized, in a formal sense it is mercury and not the thiol which is actually oxidized in these reactions. For the LCEC determination of thiols a Au/Hg amalgam electrode is used Using a series dual-electrode both thiols and disulfides can be determined in a single chromatographic experiment... 

In a simple electron transfer reaction, the reactant is situated in front of the electrode, and the electron is transferred when there is a favorable solvent fluctuation. In contrast, during ion transfer, the reactant itself moves from the bulk of the solution to the double layer, and then becomes adsorbed on, or incorporated into, the electrode. Despite these differences, ion transfer can be described by essentially the same formalism [Schmickler, 1995], but the interactions both with the solvent and with the metal depend on the position of the ion. In addition, the electronic level on the reactant depends on the local electric potential in the double layer, which also varies with the distance. These complications make it difficult to perform quantitative calculations. 

Although the extended ab initio atomistic thermodynamics approach provides an exact expression for the interfacial stability, the formalism requires self-consistent modeling of the entire electrochemical system, or electrode/electrolyte interface, exceeding presently available computational capabilities. Therefore, certain assumptions had to be made that reduce the effort to the calculation of the electrode surface only. Even with this simplified approach, which has been applied to the two examples discussed in this chapter, the qualitative behavior can be reproduced. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

According to the Nemst equation, E = E0 + (RT/F) In ([ox]/[red]) (cf., p. 29), where E0 represents the formal standard potential allowing for the direct use of concentration values within the logarithmic term, the application of a specific potential E to the electrode leads to the establishment of a certain equilibrium [ox]/[red], It is clear, that if Eappl - Em = AE becomes positive there will be a shift to greater [ox] and if negative a shift to lower [ox] than at the original ratio [ox]/[red]. 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

Obviously 0electrode potential we obtain... 

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